Kimberly Faye Greenberg pays tribute to one-time star Fanny Brice (born Fania Borach) in her solo show, “One Night With Fanny Brice,” now playing off-Broadway at St. Luke’s Theatre. Impersonating the famed Zeigfield star, Greenberg takes her from childhood to death and beyond, in a series of songs and anecdotes. Greenberg’s rich voice does credit to the songs Brice made famous, chief among them “My Man,” “Second Hand Rose,” and “Rose of Washington Square.” Thus the evening proves to be fairly entertaining.

However, though a gifted performer, Greenberg never quite becomes Brice herself. Is it that she’s too pretty? But that need not be a detriment if she had really dived into the role. The fact is that she should play Fanny more broadly, belting out the songs and speaking with a stronger Yiddish accent. (It is difficult not to make comparisons with Barbra Streisand’s portrayal of Fanny, not too long ago, in the film “Funny Girl.”)

The first act is given over to Fanny’s childhood and early years — her beloved, but no-good father, her tough, hard-working mother, and her own break into show business. Much of the bio material is interesting — her parents’ saloon in Newark, New Jersey, the parents’ battles, her starting years in burlesque, and so on.

But it is the second act in which Greenberg (and the show) comes into her own. Both Fanny and the show grow up. It covers the years of Brice’s great successes (top of her field as a singer, comedienne, stage, radio, and film actress), and her twenty years with the Zeigfield Follies. It also follows Brice into radio and her successful, long-running “Baby Snooks” show. Greenberg introduces many famed fellow performers — Eddie Cantor, W. C. Fields, Gypsy Rose Lee among them. But impersonations, alas, are not Greenberg’s strong point, and she would do better to not attempt them.

Most importantly, the second act focuses on Nicky Arnstein, the great love of Brice’s life. Arnstein, by coincience, is a larger-sized version of her father. In fact, he carries laziness, crime, gambling, exploitation, to far greater extremes. (One wonders whether Brice was seeking a father figure when she took up with Arnstein.) After six years of living together, Arnstein finally divorces his wife and marries Brice. Arnstein is several times arrested, and serves time in prison. But Brice is always behind him, paying out exorbitant funds to gain his release or lessen his discomforts in prison.

It is in the second act that Greenberg sings “My Man,” Brice’s signature piece, and it is indeed the highlight of the show. Greenberg is quite capable of offering a show-stopper, as her rendition goes from quiet, touching torch-song moments to a great roar. If only Greenberg offered more such moments throughout the show!